Sample size for a mean confidence interval using an estimated variance from a prior study

Computes the sample size required to estimate a population mean with desired confidence interval precision in applications where an estimated variance from a prior study is available. The actual confidence interval width in the planned study will depend on the value of the estimated variance in the planned study. An estimated variance from a prior study can be used to compute an upper prediction limit for the estimated variance in the planned study. The upper prediction limit is then used as the variance planning value. The probability that the prediction interval in the planned study will have a width that is less than the desired width is approximately 1 - alpha2.

This sample size approach assumes that the population variance in the prior study is very similar to the population variance in the planned study. If an estimated variance from a prior study is not available, the researcher must use expert opinion to guess the value of the variance that will be observed in the planned study. The size.ci.mean function uses a variance planning value that is based on expert opinion regarding the likely value of the variance estimate that will be observed in the planned study.

For more details, see Section 1.31 of Bonett (2021, Volume 1)

Usage

size.ci.mean.prior(alpha1, alpha2, var0, n0, w)

Arguments

alpha1: alpha level for 1-alpha1 confidence in the planned study
alpha2: alpha level for the 1-alpha2 prediction interval
var0: estimated variance in prior study
n0: sample size in prior study
w: desired confidence interval width

Value

Returns the required sample size

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

size.ci.mean.prior(.05, .10, 0.71, 204, .4)
#>  Sample size
#>           88

# Should return:
# Sample size
#          88